Using technology to support diagrammatic reasoning about center and variation.

We conducted two design experiments aimed at engaging sixth graders (11 years old) in statistical reasoning about center and variation. We examine in particular students' informal notion of a "modal clump." Using Peirce's concept of diagrammatic reasoning, we analyze the interplay of 1) making plots with TinkerPlots - a computer data analysis tool, 2) experimenting with those plots, and 3) developing a language to talk about features of the data sets as represented in the plots by reflecting on judgments. More generally, we draw on Brandom's recent work in philosophy to argue that an "inferential" view should be privileged over a "referential" view of teaching and learning statistics.